Merchant Marine Cargo Operations, Plimsoll Load Lines & Hydrostatics
Ship Tons Per Centimeter (TPC) & Freshwater Allowance Formula
Calculate Saltwater Tons Per Centimeter Immersion TPC (t/cm), Plimsoll Freshwater Allowance FWA (mm), Brackish Dock Water Allowance DWA (mm), and Extra Permissible Cargo Mass (t).
Loading to the Plimsoll Dock Water Allowance in brackish river ports—because hull draft rises automatically once out in 1.025 t/m³ ocean seawater!
Chief officers loading bulk carriers in river/estuary ports (dock water density rho_dock between 1.000 and 1.025 t/m³) are legally permitted under the International Load Line Convention to submerge the Summer Plimsoll Mark S by the Dock Water Allowance (DWA, mm)—because Archimedes buoyancy guarantees the hull will bodily rise back to exact Summer draft upon entering standard 1.025 t/m³ ocean seawater! For waterplane area A_w (m²), Saltwater Tons Per Centimeter Immersion is TPC_sw = (A_w * 1.025) / 100 (metric tons per cm sinkage), Pure Freshwater Allowance is FWA = Displacement_t / (4 * TPC_sw) mm (derived from 10 mm/cm divided by 40, since (1.025 - 1.000) / 1.000 = 1/40!), and Brackish Dock Water Allowance is DWA = FWA * ((1.025 - rho_dock) / 0.025) mm!
Verify on a 52,000-Ton Displacement Supramax Bulk Carrier—Waterplane_Area A_w = 4,200.0 m² (B2), Summer_Displacement = 52,000.0 t (B3), and Estuary_Dock_Density rho_dock = 1.005 t/m³ (B4): Saltwater TPC hits (4,200 * 1.025) / 100 = 43.05 t/cm (E2), Plimsoll Freshwater Allowance FWA equals 52,000 / (4 * 43.05) = 301.97 mm (E3), Brackish Dock Water Allowance DWA equals 301.97 * ((1.025 - 1.005) / 0.025) = 241.58 mm (E4 = 24.158 cm), and Dock TPC (4,200 * 1.005 / 100 = 42.21 t/cm) allows submerging 24.158 cm deeper in brackish river water while emerging at exact Summer Mark at sea (E5 shows Dock TPC = 42.21 t/cm)!
| Plimsoll Hydrostatics KPI (Aw = 4,200 m², Disp = 52,000 t, Dock = 1.005 t/m³) | Formula | Verified Output |
|---|---|---|
| Saltwater Immersion TPC_sw (t/cm) | (Waterplane_Area_m2 * 1.025) / 100 | 43.05 t/cm |
| Freshwater Allowance FWA (mm) | Displacement_t / (4 * TPC_sw) | 301.97 mm |
| Dock Water Allowance DWA (mm) | FWA * ((1.025 - Dock_Density) / 0.025) | 241.58 mm (301.97 @ 1.000 river) |
| Actual Dock Immersion TPC_dock | (Waterplane_Area_m2 * Dock_Dens) / 100 | 42.21 t/cm (42.00 @ 1.000 river) |
Plimsoll Load-Line Freshwater & Brackish Dock Water Allowance Formula
Validate Waterplane_Area A_w > 0, Displacement > 0, and Dock_Density in [1.000, 1.025] t/m³!
=LET(aw_m, B2, ds_t, B3, rd_k, B4, IF(OR(aw_m <= 0, ds_t <= 0, rd_k < 1, rd_k > 1.025), "Invalid Hydrostatic Input", LET(tp_s, (aw_m * 1.025) / 100, fw_a, ds_t / (4 * tp_s), ROUND(fw_a * ((1.025 - rd_k) / 0.025), 2))))Pure Freshwater Upriver Terminal Full FWA Check (Set Dock Density = 1.000 t/m³)
Load upriver in pure freshwater (Dock_Density B4 = 1.000 t/m³): Dock Water Allowance E4 expands to the full Plimsoll FWA of 301.97 mm while Dock TPC E5 adjusts to 42.00 t/cm!
=IF(ISTEXT(E4), E4, ROUND((B2 * B4) / 100, 2))Try the example
Use the original values or change them to test your understanding.